Officially, at least, the 1,600 people who gathered in the snow on Dresden's Ammonstrasse were not attending a neo-Nazi demonstration. It was a March of Mourning, held, according to the paperwork submitted to Dresden council, to commemorate the Germans killed by allied bombs 67 years previously.

You do not have to be a rightwing extremist to question the carpet bombing that flattened Dresden during two days in February 1945. Or, many would argue, to pay respects to the many thousands who died in 1,600C heat as the city burned.

But the rally was not without undertones: the burning torches evocative of the scenes portrayed by Leni Riefenstahl in Triumph of the Will, her 1934 propaganda documentary about the Nuremberg rallies; the hooded tops with slogans such as Weisse Willen (the will of whites); the banners referring to the "bombing holocaust"; or indeed the red, white and black flags waved during the Third Reich.

It all seemed to justify the several thousand antifascist campaigners who were noisily blockading streets around the corner, or the 13,000 locals who had formed a human chain around the rebuilt Frauenkirche in the town centre.

The marchers have been clashing with counter-demonstrators in Dresden for years. But this year, tensions were particularly high following the discovery in November of an alleged neo-Nazi terror cell calling itself the National Socialist Underground (NSU) whose members, with apparent impunity, aare said to have killed nine immigrants and one police officer during 11 years on the run.

On Thursday, Angela Merkel attended a memorial service for the victims in Berlin, calling the murders a "disgrace for our country".

In the three months since the news broke, there has been ample evidence to suggest Germany's far right has been celebrating rather than condemning the killing spree.

At a fascist march in Munich in January, demonstrators blasted the Pink Panther theme tune from loudspeakers, a reference to bizarre videos featuring the cartoon character which the group produced.

Just a few weeks after two core members of the group were found dead in a camper van after an apparent double suicide, football supporters in Zwickau, the eastern town where the NSU members had been living under false identities, chanted "Terrorzelle Zwickau – ole, ole, ole". A footballer from FSV Zwickau was fined after responding to shouts of "Sieg!" from the crowd during the same match with "Heil!".

By the German government's latest estimate, from 2010, there are 9,500 rightwing extremists in Germany who are "ready to commit violence". That year, 16,375 "rightwing-motivated" crimes were recorded.

The perpetrators are not as easy to spot as they were in the late 1990s, when Uwe Mundlos and Uwe Böhnhardt, two of the key NSU trio, were photographed at neo-Nazi marches with shaved heads, wearing bomber jackets and boots with white shoelaces, their trousers held up with red, black and white braces.

These days, the easiest way to spot someone with far-right leanings is if they are wearing something from Thor Steinar, a Nordic-inspired German brand whose shops are constantly picketed by anti-Nazi campaigners.

Previously, German neo-Nazis favoured the British boxing make Lonsdale, largely because if the logo was partly obscured beneath a bomber jacket, only the initials NSDA were visible – one letter short of Hitler's Nazi party, the National Sozialistische Deutsche Arbeiter Partei.

Lonsdale has long gone out of fashion among rightwingers after the brand produced an advertising campaign featuring black footballers saying "Lonsdale loves all colours" in an explicit attempt to put off its most loyal customers.

At the march earlier this month, everyone the Guardian spoke to said they were not a neo-Nazi and would not be named for fear of being labelled as such. "I'm a patriot," said one 29-year-old who had his hood up and had covered his face with a scarf.

But German neo-Nazis are not always so circumspect. Well-publicised internet "hitlists" target leftwing politicians, pubs and social projects. There have been at least 182 murders motivated by rightwing extremism since German reunification in 1990, according to the Antonio Amadeu foundation pressure group. The government put the figure at just 47 in December, though some states are now increasing their own numbers after going back through their files.

Among the general population, intolerance is on the increase. A long-term study by the sociologist Wilhelm Heitmeyer in 2011 showed that every second German believes too many foreigners live in Germany, and 53% would have a problem moving into an area where lots of Muslims lived, an increase of 6% from 2004.

Against this backdrop of tacit racism it is no wonder that detectives appear not to have bothered to investigate rightwing extremism as a possible motive for the 10 killings, according to Katina Schubert, an expert in race relations from the leftwing Die Linke party.

"It's clear the police and intelligence agencies were racist to the core," she claimed. "They assumed right from the start that the eight Turks and one Greek man were killed by members of their own immigrant communities. The police briefed that these men were embroiled in drug smuggling plots or other crimes."

Until the group was uncovered in November, the killings were known in Germany as the "doner murders", which incorrectly gave the impression all the dead men were kebab sellers, reinforcing the stereotype that that's what Turks in Germany do.

In Berlin on Thursday, Merkel apologised to the families of those killed. "For years, some relatives themselves unfairly faced suspicion that is particularly oppressive," said the chancellor. "I ask for forgiveness for that."

The police in Germany are "blind in the right eye", say critics. "A 17-year-old in Nuremberg, where I live, was almost beaten to death by a neo-Nazi and the police didn't take it at all seriously," said Idil, a 19-year-old student attending an anti-Nazi counter-march in Dresden earlier this month. The boy, a Kurdish friend of hers, was left for dead in April 2010 after remarking on a Thor Steinar accessory carried by his attacker's girlfriend.

Extreme rightwingers are not only operating in the shadows – some of them sit in state parliaments as representatives of the National Democratic party (NPD). Interior ministers at local and national levels are looking at the logistics and possible consequences of banning the party after two former members were arrested on suspicion of helping the NSU during their 11 years on the run.

The NPD's top brass deny all links with terrorism. But they do not try hard to hide their Nazi sympathies: a recent report in Der Spiegel noted that the Germanic Elhaz rune, the symbol of the Third Reich's "Lebensborn" programme, which supported the production of racially pure Aryan children, hangs above the entrance of their office.

It is not hard to find brazen neo-Nazis in Germany if you know where to look.

It was just gone seven on a recent night in Berlin when half a dozen drinkers summoned an American man over to their table in a Berlin pub. It had been happy hour since 5pm: €1.50 (£1.25) for half a litre of pilsner. "Hey New York, komm her!" said one black-clad customer in Zum Henker (To the Executioner), a windowless pub in the eastern district of Schöneweide.

After a bit of chit-chat, glasses were raised. "Prost!" said the American. He clinked his stein against his neighbour's, expecting the German man to respond in kind. Instead, his new acquaintance raised his right arm and bellowed "Sieg Heil!" to much amusement from the crowd of men, all in their late teens or 20s.

Zum Henker is often described as a key meeting place for rightwing extremists in Berlin. Its British owner, Paul Barrington, a well-spoken, portly skinhead, welcomed the Guardian to his establishment in a T-shirt advertising Combat 18, the British neo-Nazi terror organisation. There is no suggestion any of the NSU terrorists ever visited Zum Henker or had connections to it, or that Barrington, who grew up around Plumstead in south-east London before moving to the German capital 20 years ago, was linked in any way to the terror cell.

But the confidence with which Barrington and his customers display their Nazi sympathies is evidence, say campaigners, that Germany's far right no longer hides in the shadows but is swaggering into clearer view.

Take the landlord himself. Eight years ago, Barrington was prosecuted after posting a picture on his website of an undercover policeman and captioning it with "this bullet is for you". Barrington now says the caption was simply a quote from a "well-known song".

Today he still likes playing with words and numbers. A popular cocktail on sale at his pub is the Himla, made with raspberry rum, and paying homage to Heinrich Himmler, the Nazi police chief. The numbers on his T-shirt translate as Adolf Hitler (A=1, H=8). Tomorrow Barrington will host one of his most popular parties, where drinks cost just 88 cents. It's just a "promotion for people with not so much money at the end of the month", he said.

Yes, he conceded in an email later, the Himla "could be seen as a provocation, but people remember it and it has turned out to be one of the most talked about drinks in Berlin. Do not forget we are a pub and not a party political headquarters. We do not have to be politically correct." As for the Sieg Heil-ing, perhaps we had misheard. Could they not have said "schmeckt geil!" (tastes great!)?

In an email, we asked Barrington if he condemned the immigrant murders. His answer: "No comment."

• Flaunting Mein Kampf in public, giving it unnecessary prominence in a shop window or lauding its ideas can fall foul of German laws

Legal

• All the illegal symbols, greetings and slogans can be used legitimately if for "creditable purposes". For example, an anti-Nazi T-shirt showing a swastika being crossed out or put in the bin, or if used in the context of a museum exhibition, history book, art or satire

• Having pictures, busts or sculptures of other Nazi figures, for example Rudolf Hess or Heinrich Himmler

• Goose-stepping without the outstretched arm

• Singing the Nazi national anthem, Das Deutschlandlied – it is still the German national anthem today, but now only the third verse is used, omitting the most famous "Deutschland, Deutschland über alles" stanza

• Owning a copy of Mein Kampf or selling it in a second-hand book shop

• The Illegal/Legal article was corrected on 24 February 2012 because the original version said that owning Mein Kampf remains illegal in Germany. The last point in each category above has been amended accordingly.